function to describe a graph

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I have a graph that looks like this.

picture

I would like to know how to define this as a function. Any help would be greatly appreciated.

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In general you cannot infer/deduce an exact single formula
(analytical representation) just from a graph like the one
you have.

Instead you can discretize the points on the X axis,
and then use some polynomial, or (better) a set of polynomials
i.e. a spline to approximate it your function.
The more points you pick on the X axis, the better the approximation would be.

See also:

Splines